A321665 - OEIS

%I #30 Dec 22 2020 10:04:52

%S 1,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,1,0,2,0,2,2,2,0,3,1,3,2,4,1,5,2,5,4,

%T 6,4,9,3,8,7,10,6,13,7,13,12,16,10,20,13,22,19,24,18,32,23,34,30,37,

%U 30,49,37,50,47,58,51,73,58,77,74,89,80,108,91,116

%N Number of strict integer partitions of n containing no 1's or prime powers.

%H Vaclav Kotesovec, <a href="/A321665/b321665.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..500 from Fausto A. C. Cariboni)

%F G.f.: Product_{k>=2, k not a prime power} 1 + x^k. - _Joerg Arndt_, Dec 22 2020

%e The a(36) = 9 strict integer partitions:

%e   (36)

%e   (30,6)

%e   (21,15)

%e   (22,14)

%e   (24,12)

%e   (26,10)

%e   (18,12,6)

%e   (20,10,6)

%e   (14,12,10)

%t nn=100;

%t ser=Product[If[PrimePowerQ[n],1,1+x^n],{n,2,nn}];

%t CoefficientList[Series[ser,{x,0,nn}],x]

%Y Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A321346, A321347, A321378, A322452, A322454.

%K nonn

%O 0,19

%A _Gus Wiseman_, Dec 11 2018